Question

projectile motion
the trajectory of a kicked football
use the picture above to answer the calculation. suppose the football player kicks the football with an initial velocity of 100 m/s and at an angle of 30°. calculate the vertical and horizontal components of initial velocity.
a
vₓ=50m/s
vᵧ=87m/s
b
vₓ=87m/s
vᵧ=50m/s
c
vₓ=58m/s
vᵧ=50m/s
d
vₓ=58m/s
vᵧ=87m/s

Explanation:

Step1: Recall velocity components formula

For projectile motion, horizontal (\(v_x\)) and vertical (\(v_y\)) components of velocity are given by \(v_x = v_0\cos\theta\) and \(v_y = v_0\sin\theta\), where \(v_0 = 100\,\text{m/s}\) and \(\theta = 30^\circ\).

Step2: Calculate horizontal component

\(v_x = 100\cos(30^\circ)\). Since \(\cos(30^\circ)=\frac{\sqrt{3}}{2}\approx0.87\), \(v_x = 100\times0.87 = 87\,\text{m/s}\).

Step3: Calculate vertical component

\(v_y = 100\sin(30^\circ)\). Since \(\sin(30^\circ)=\frac{1}{2}=0.5\), \(v_y = 100\times0.5 = 50\,\text{m/s}\).

Answer:

B. \(v_x=87\,\text{m/s}\), \(v_y=50\,\text{m/s}\)